1. If the employer wins the lawsuit it gets a judgment for whatever amount the court says you owe the employer. Note that in Texas the law is a bit different than in most states in that if this lawsuit is based on breach of contract the winning side gets to add attorney’s fees and other costs to the judgement, so it could end up being a fair bit more than $110,000 by the time it’s all done. Once the court issues the judgement, the employer may seek to collect that judgment by attaching any assets or income that you have that is not exempt under federal and state law. The court will not get involved with whether you may make payments on this; that will be totally up to the employer if it wins the judgment against you.
2. Texas is just one of 4 states that does not allow garnishment of wages to collect a private judgment. The problem, though, is that you are the sole member of a LLC. How that gets treated varies from state to state, and it is possible that in Texas the funds you take out of the LLC would not be considered “wages” but rather distributions and those distributions would not be protected by the prohibition on wage garnishment. I have not researched Texas court decisions on that, and you ought to ask your lawyer about it. (And if you are being sued for $110k you really ought to have a lawyer advising you.)

